Knowledge Representation via Verbal

Description Generalization:

Alternative Programming in Sampletalk

Language

Andrew Gleibman

Sampletalk Research

https://sampletalk.github.io/

Knowledge Representation via Verbal

Description Generalization:

Alternative Programming in Sampletalk

Language

Sampletalk Technology:

Alternative Logic

Alternative Syntax & Semantics

Alternative NLP

Andrew Gleibman

Sampletalk Research

https://sampletalk.github.io/

Definition of the Alternative

Programming via a Metaphor:

Conventional Programming

Formal Grammar Theory

DB theory

Logic

Calculus

…

Conventional Medicine

Chemistry

Physics

Electronics

Mechanics

…

Alternative Medicine

Natural Preparations

as Healing Means;

Natural Adaptation of the

Organism to the Environment

Alternative Programming

Patterns of Natural Texts

as Programming Means

Alignment, Structurization, Generalization

and Composition of Natural Texts

Aligned Reasoning

What can John see? A book

What can Mary see? The red table

what can [A] see? [X]

Generalized Reasoning

Aligned Facts

John can see a book

Mary can see the red table

[A] can see [X]

Generalized Pattern of the Facts

The Composed Sampletalk Clause:

what can [A] see? [X] :–[A] can see [X]..

Alignment, Structurization, Generalization

and Composition of Natural Texts:

Generalization

Question Answer

Instantiated program clause

Program clauses

, …

:-- , …

Subgoal

Goal

Subgoal

…

Head

Subgoal

New goal

…

Fact

:--

Head

Fact

Head

Unification

A scheme of a logic program

Instantiated program clause

Program clauses

, …

:-- , …

Subgoal

Goal

Subgoal

…

Head

Subgoal

New goal

…

Fact

:--

Head

Fact

Head

Unification

In Prolog:

Logical Atoms

A scheme of a logic program

Instantiated program clause

Program clauses

, …

:-- , …

Subgoal

Goal

Subgoal

…

Head

Subgoal

New goal

…

Fact

:--

Head

Fact

Head

Unification

In Prolog:

Logical Atoms

In Sampletalk:

Unrestricted

Generalized Texts

A scheme of a logic program

Facts:

[book] is in [open box]..

[notebook] is in [closed box]..

[open box] is on [red table]..

[closed box] is on [red table]..

[john] has approached [red table]..

Logico-linguistic inference rules:

can [A] see [X]? :–[A] can see [X]..

what can [A] see? [X] :–[A] can see [X]..

what is in [A]? [X] :–[X] is in [A]..

what is visible on [A]? [X] :–[X] is visible on [A]..

what is invisible on [A]? [X] :–[X] is in [B] ,, [B] is on [A] ,, ~~[X] is visible on [A]..

what is on [A]? [X] :–[X] is on [A]..

what is on [A]? [X] :–[X] is in [B] ,, [B] is on [A]..

[A] can see [X] :–[A] is standing near [B] ,, [X] is visible on [B]..

[A] is visible on [B] :–[A] is on [B]..

[A] is visible on [B] :–[A] is in [open X] ,, [open X] is visible on [B]..

[A] is standing near [B] :–[A] has approached [B]..

Sampletalk Program Example:

Negation

Facts:

[book] is in [open box]..

[notebook] is in [closed box]..

[open box] is on [red table]..

[closed box] is on [red table]..

[john] has approached [red table]..

Logico-linguistic inference rules:

can [A] see [X]? :–[A] can see [X]..

what can [A] see? [X] :–[A] can see [X]..

what is in [A]? [X] :–[X] is in [A]..

what is visible on [A]? [X] :–[X] is visible on [A]..

what is invisible on [A]? [X] :–[X] is in [B] ,, [B] is on [A] ,, ~~[X] is visible on [A]..

what is on [A]? [X] :–[X] is on [A]..

what is on [A]? [X] :–[X] is in [B] ,, [B] is on [A]..

[A] can see [X] :–[A] is standing near [B] ,, [X] is visible on [B]..

[A] is visible on [B] :–[A] is on [B]..

[A] is visible on [B] :–[A] is in [open X] ,, [open X] is visible on [B]..

[A] is standing near [B] :–[A] has approached [B]..

Sampletalk Program Example:

Exploiting the Natural Syntax &

Semantics of the Original NL Phrases

rather than

Inventing an Artificial Syntax and

Making an Artificial Semantic Model

Negation

Example Inputs:

1) can [john] see [book]?

2) can [john] see [notebook]?

3) can [john] see [open box]?

4) what can [john] see? [X]

5) what is visible on [red table]? [X]

6) what is invisible on [red table]? [X]

7) what is on [red table]? [X]

8) what is in [open box]? [X]

9) what is in [closed box]? [X]

The Outputs:

1) can [john] see [book]? Yes.

2) can [john] see [notebook]? No.

3) can [john] see [open box]? Yes.

4) what can [john] see? [open box]. Yes;

what can [john] see? [closed box]. Yes ;

what can [john] see? [book]. Yes.

5) what is visible on [red table]? [open box]. Yes;

what is visible on [red table]? [closed box]. Yes;

what is visible on [red table]? [book]. Yes.

6) what is invisible on [red table]? [notebook]. Yes.

7) what is on [red table]? [open box]. Yes;

what is on [red table]? [closed box]. Yes;

what is on [red table]? [book]. Yes;

what is on [red table]? [notebook]. Yes.

8) what is in [open box]? [book]. Yes.

9) what is in [closed box]? [notebook]. Yes.

NL Query

Formal Representation

of the Query

Inference Engine,

Ontology,

Formal Model

Formal Response

Parsing

NL Phrase

Generation

NL Response

Common FOL+NLP approach: The need to design predicates,

grammars, a semantic model, and implement a parser,

a formal reasoning engine and a NL phrase generator

NL Query

Inference Engine,

Ontology,

Formal Model

NL Response

The alternative NLP approach: No predicates, no grammars,

no artificial semantics, no parsers. Everything is defined via

immediate interaction of patterns of the existing NL phrases.

The alternative NLP approach: No predicates, no grammars,

no artificial semantics, no parsers. Everything is defined via

immediate interaction of patterns of the existing NL phrases.

Logico-linguistic inference rules:

can [A] see [X]? :–[A] can see [X]..

what can [A] see? [X] :–[A] can see [X]..

what is in [A]? [X] :–[X] is in [A]..

what is visible on [A]? [X] :–[X] is visible on [A]..

what is invisible on [A]? [X] :–[X] is in [B] ,, [B] is on [A] ,, ~~[X] is visible on [A]..

what is on [A]? [X] :–[X] is on [A]..

what is on [A]? [X] :–[X] is in [B] ,, [B] is on [A]..

[A] can see [X] :–[A] is standing near [B] ,, [X] is visible on [B]..

[A] is visible on [B] :–[A] is on [B]..

[A] is visible on [B] :–[A] is in [open X] ,, [open X] is visible on [B]..

[A] is standing near [B] :–[A] has approached [B]..

Advantages of Alternative Programming --

Logico-Linguistic Inference:

Ontology:

Set of NL phrase patterns

with model usage of terms

Query: NL phrase pattern

Inference and Linguistic Knowledge:

Representation of inferences in the form of

generalized verbal descriptions

Response: NL phrase

Current Knowledge:

Representation of facts in

the form of verbal

descriptions

The alternative NLP approach: No predicates, no grammars,

no artificial semantics, no parsers. Everything is defined via

immediate interaction of patterns of the existing NL phrases.

Advantages of Alternative Programming --

Logico-Linguistic Inference:

can [john] see [book]? Goal

Explanation:

1 [open box] is on [red table], DB Fact

2 [open box] is visible on [red table], From 1

3 [book] is in [open box], DB Fact

4 [book] is visible on [red table], From 2,3

5 [john] has approached [red table], DB Fact

6 [john] is standing near [red table], From 5

7 [john] can see [book]. From 6,4

can [john] see [book]? Yes From 7

Advantages of Alternative Programming --

Generating Verbal Explanation of the Sampletalk Reasoning:

Advantages of Alternative Programming -- Inheritance of the

Syntax and Semantics from the Original NL Phrases:

Predicate Notation Sampletalk Notation

hasChild (anna, jacopo)

is_in (book, open_box)

is_in (notebook, closed_box)

is_on (open_box, red_table)

is_on (closed_box, red_table)

has_approached (john, red_table)

can_see (X,Y)

is_visible_on (X,Y)

is_standing_near (X,Y)

[jacopo] is child of [anna]

[anna] has child [jacopo]

[anna] is parent of [jacopo]

[book] is in [open box]..

[notebook] is in [closed box]..

[open box] is on [red table]..

[closed box] is on [red table]..

[john] has approached [red table]..

[A] can see [B]

[A] is visible on [B]

[A] is standing near [B]

Algorithmic properties of Sampletalk language –

Turing completeness: Any Markov algorithm can be

represented as a Sampletalk theory:

THEOREM:

Let M be any Markov algorithm written in a base alphabet U and a local

alphabet V, where (U V) L and L is the alphabet of terminal symbols

applied in text theories.

There exists a text theory PM, which, given a goal [ξtξ][W] (where t is a

string, ξand are terminal symbols not belonging to alphabets U and V,

Wis a variable), does the following:

Transforms the goal into a text [ξtξ][ξt′ξ] and stops if M

transforms string t into a string t′and stops;

Produces a text [ξtξ][[fail]] and stops if no rule of Mis

applicable to some derivation of t, produced by M;

Never stops if string t leads M to an infinite application of the

Markov rules.

Algorithmic properties of Sampletalk Language --

Alternative Version of the Church-Turing Thesis

THESIS 2 (no previous generalization needed):

Every effective computation can be carried out using a set

of pairs of similar data examples and a limited set of rules

for combining such pairs and the input data.

THESIS 1.

Every effective computation can be carried out using

generalized patterns of some data examples and a limited set

of rules for combining such patterns and the input data.

Philosophical aspects of the Sampletalk Technology

Sampletalk as the generalization of Prolog

Alternative Logic as the generalization of Predicate Logic.

Unification of the generalized texts (axioms) defines the inference

Discussion

Alternative Programming:

Prolog Sampletalk

Alternative Logic:

First Order Predicate Calculus First Order Text Calculus

Artificial Semantics vs. Alternative Semantics

Application issues of the two ways to

build a semantic model

should be analyzed

a book is in an open box

a notebook is in a closed box

cat is in the cage

a fox is in zoo

john is in his red car

this large table is red

a [X] is in [D] [Y] box

[X] is in [D] [Z]

a [X] is in [Z]

[X] is in [Z]

[X] is [A]

Pair-wise Alignment and Generalization of a Corpus of

Sentences:

Discussion (Continued)

A building material for constructing

Sampletalk theories for NLP

E+= {(si, ti): i = 1, 2, …,n} (positive examples)

E–= {(s′j, t′j): j = 1, 2, …,m} (negative examples)

f(Q) = ( |{(si, ti)E+: Q(si) = ti}| –|{(s′j, t′j)E–: Q(s′j) = t′j}| ) / |Q|,

where Q is a Sampletalk theory;

P = argmax (f(Q))

Machine-Learning Setting –

Extracting Sampletalk Theories from Examples:

Discussion (Continued)

A set of positive and negative text examples:

Objective function for learning a Sampletalk theory P:

Theory of the above set of examples:

A set of positive and negative text examples:

[[a + b]] [+ ab]

[[x + y]] [+ xy]

¬[[u + v]] [u +v]

[[a]] [a]

[[x]] [x]

[[a +[b + c]]] [+ a + b c]

[[u –v]] [–uv]

[[e +[f + g]]] [+ e + f g]

[[e +[f –g]]] [+ e–fg]

[[e /[f –g]]] [/ e–fg]

[[[a +b] + c]] [+ + a b c]

[[[a1 / b2] + c3]] [+ / a1 b2 c3]

[[a * b]] [* ab]

[[[a +b] *[c –d]]] [* + a b –cd]

Machine-Learning Setting –

Extracting Sampletalk Theories from Examples:

Discussion (Continued)

[[A Z B]] [Z C D] :-- [[A]] [C] ,, [[B]] [D]..

[[A]] [A]..

Suggested Research:

1) Experiments with automatic Sampletalk theory generation for

specific data (e.g., geographical, biological) and applications;

2) Alignment of Non-Text Data: FOPC FOTC FOIC FOOC

First Order Predicate Calculus

Discussion (Continued)

First Order Text Calculus

First Order Image Calculus

First Order Object Calculus

The Theory:

result of morphological analysis of word [X i e d]: this is past form of verb "X y" :–

word “X y” has canonical morphological tag “verb”..

result of morphological analysis of word [X ed]: this is past form of verb "X e" :–

word “X e” has canonical morphological tag “verb”..

result of morphological analysis of word [X e d]: this is past form of verb "X" :–

word “X” has canonical morphological tag “verb”..

result of morphological analysis of word [X i e s]: this is 2-sg form of verb "X y" :–

word “X y” has canonical morphological tag “verb”..

result of morphological analysis of word [X es]: this is 2-sg form of verb "X e" :–

word “X e” has canonical morphological tag “verb”..

Goal:

result of morphological analysis of word [q u e r i e s]: this is X.

The Outputs:

result of morphological analysis of word [q u e r i e s]: this is 2-sg form of verb "q u e r y";

result of morphological analysis of word [q u e r i e s]: this is plural form of noun "q u e r y".

Additional Sampletalk Theory Example:

A Theory of Morphological Analysis

Continued

result of morphological analysis of word [X s]: this is 2-sg form of verb "X" :–

word “X” has canonical morphological tag “verb”..

result of morphological analysis of word [X i e n]: this is past-p form of verb "X y" :–

word “X y” has canonical morphological tag “verb”..

result of morphological analysis of word [X e n]: this is past-p form of verb "X e" :–

word “X e” has canonical morphological tag “verb”..

result of morphological analysis of word [X e n]: this is past-p form of verb "X" :–

word “X” has canonical morphological tag “verb”..

result of morphological analysis of word [X y i n g]: this is ing-form of verb "X y" :–

word “X y” has canonical morphological tag “verb”..

result of morphological analysis of word [X i n g]: this is ing-form of verb "X e" :–

word “X e” has canonical morphological tag “verb”..

result of morphological analysis of word [X i n g]: this is ing-form of verb "X" :–

word “X” has canonical morphological tag “verb”..

result of morphological analysis of word [X]: this is canonical verb form "X" :–

word “X” has canonical morphological tag “verb”..

result of morphological analysis of word [X i e s]: this is plural form of noun "X y" :–

word “X y” has canonical morphological tag “singular noun”..

result of morphological analysis of word [X es]: this is plural form of noun "X e" :–

word “X e” has canonical morphological tag “singular noun”..

Continued

result of morphological analysis of word [X s]: this is plural form of noun "X" :–

word “X” has canonical morphological tag “singular noun”..

result of morphological analysis of word [X]: this is canonical singular form of noun "X" :–

word “X” has canonical morphological tag “singular noun”..

result of morphological analysis of word [X]: this is adverb "X" :–

word “X” has canonical morphological tag “adverb”..

result of morphological analysis of word [X]: this is adjective "X" :–

word “X” has canonical morphological tag “adjective”..

…

word “b a c k” has canonical morphological tag “singular noun”..

word “b a c k” has canonical morphological tag “adverb”..

word “b a c k” has canonical morphological tag “verb”..

word “b a k e” has canonical morphological tag “singular noun”..

word “b a k e” has canonical morphological tag “verb”..

word “b a k e r” has canonical morphological tag “singular noun”..

word “b a k e r y” has canonical morphological tag “singular noun”..

word “q u e r y” has canonical morphological tag “singular noun”..

word “q u e r y” has canonical morphological tag “verb”..

…

The goal (variable W stands for the transformation result):

(x0)[a(x0,y)] \/ (x0)[b(x0,t)] --> W..

The theory:

(Q X)[F] \/ (Q X)[H] --> (Q X)(Q Z)([F] \/ [G]) :–

X is variable,,

Z is variable,,

not(F contains Z),,

(Z/X)[H]=[G]..

x0 is variable..

X10 is variable :–X0 is variable..

AXB contains X..

(Y/X)[AXM]=[AYN] :- (Y/X)[M]=[N]..

(Y/X)[A]=[A]..

The result:

(x0)[a(x0,y)] \/ (x0)[b(x0,t)] --> (x0)(x10)([a(x0,y)] \/ [b(x10,t)]).

Additional Sampletalk Theory Example --

A Theory for Logic Formula Transformation:

The goal (variable W stands for the transformation result):

according to the rule R, the result of shifting quantifiers

in the formula (x0)[a(x0,y)] \/ (x0)[b(x0,t)] is formula W..

The program:

according to the rule 2a from chapter 5, the result of shifting quantifiers

in the formula (Q X)[F] \/ (Q X)[H] is formula (Q X)(Q Z)([F] \/ [G]) :-

X is notation for variable,,

Z is notation for variable,,

not(word F contains word Z),,

the result of replacing X by Z in formula H is G..

x0 is notation for variable..

X10 is notation for variable :- X0 is notation for variable..

word AXB contains word X..

the result of replacing X by Y in formula AXM is AYN :-

the result of replacing X by Y in formula M is N..

the result of replacing X by Y in formula A is A..

The result:

according to the rule 2a from chapter 5, the result of shifting quantifiers in the formula

(x0)[a(x0,y)] \/ (x0)[b(x0,t)] is formula (x0)(x10)([a(x0,y)] \/ [b(x10,t)]).

Additional Sampletalk Theory Example --

Another Theory for Logic Formula Transformation: